Reconstruction of turbo-code encoders

Turbo-code encoders are one of the spreadest family of error correcting codes used in the communication's world, especially in space transmissions. This paper presents an efficient technique to reconstruct turbo-code encoders which allows a passive adversary, with only few bits of an intercepted message encoded by the target turbocode encoder, to determine the parameters of the turbo-code encoder used, and therefore to decode online the communications. Thereby, our results confirm that keeping secret the parameters of turbo-code encoders can not be considered as a cryptographically way to ensure confidentiality. The starting point of our work is algorithms due to Filiol which enable to find the parameters of each convolutional encoder in the turbo-code encoder. Then, we recover the interleaver with two new algorithms, the first one based on the dynamic trie structure and the second one on a first order statistical test. The first algorithm is dedicated to noiseless channels. The asymptotic complexity of the complete process is O(n4) when a n2-bit message is available to attack a n-bit turbo-code encoder. The second algorithm works for every kind of channel and the noise does not matter much. Additionally, we present experimental results which underline the right detection threshold to use to recover the interleaver with a high probability. Furthermore, this method also works for turbo-code encoders composed of punctured convolutional encoders.